Investment Strategy
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INVESTMENT STRATEGY
Given: Client’s portfolio for the investment:•
Growth stock fund
•
Income fund
•
Money market fund
Overall risk-index = weighted average of risk ratings of 3 funds. Max risk index assigned for the client = .05 Total amount to be invested = $800,000 Type of fund GSF IF MMF
% amount invested of total amount 20 TO 40 20 TO 50 ATLEAST 30
Risk rating
Expected yield (%)
.10 .07 .01
18 12.5 7.5
SOLUTION:Let the decision variables be X1 = Amount invested in growth stock fund. X2 = Amount invested in investment fund. X3 = Amount invested in money market fund. The objective function (FOR THE MAXIMIZATION OF YIELD) will be Max Z = .18X1 + .125X2 + .075X3. Subjected to the constraints:1. 160000 <= X1 <=320000 2. 160000 <= X2 <= 400000
3. X3 =>240000
4. (.1X1 + .07X2 + .01X3)/ (X1 + X2 + X3) <=.05 5. X1 + X2 + X3 =800000 1. On solving the above equations using management scientist, for the maximum yield, we have X1 = 248888, X2 = 160000, X3 = 391111 Z = 94133.33
2. Our new objective function is – Max Z = .18X1 + .125X2 + .075X3. And constraints are1. 160000 <= X1 <=320000 2. 160000 <= X2 <= 400000 3. X3 =>240000 4. (.1X1 + .07X2 + .01X3)/ (X1 + X2 + X3) <=.055 5. X1 + X2 + X3 =800000 On solving we getX1 = 293333, X2 = 160000, X3 = 346666 Z = 98800
3. Constraints are1. 160000 <= X1 <=320000 2. 160000 <= X2 <= 400000 3. X3 =>240000 4. (.1X1 + .07X2 + .01X3)/ (X1 + X2 + X3) <=.05 5. X1 + X2 + X3 =800000
A. New objective function isMax Z =.16X1+.125X2+.075X3
On solving we getX1=248888, X2=160000, X3=391111 Z= 89155
B. New objective function isMax Z=.14 X1 +.125 X2 +.075 X3 On solving we getX1=160000, X2=293333, X3=346666 Z=85066
4. Objective function isMax Z = .18X1 + .125X2 + .075X3. Subjected to the constraints:1. 160000 <= X1 <=320000 2. 160000 <= X2 <= 400000 3. X3 =>240000 4. (.1X1 + .07X2 + .01X3)/ (X1 + X2 + X3) <=.05 5. X1 + X2 + X3 =800000 6. X1<=X2
On solving this we getX1=213333, X2=213333, X3=373333 Z=93066
5. According to our recommendation, it is possible to use this model between the ranges:1. 15% < GROWTH STOCK FUND YIELD < NO LIMIT 2. NO LIMIT < INCOME FUND YIELD < 14.5% 3. 1.5% < MONEY MARKET FUND YIELD < 18%.
If the expected yield crosses these ranges, the model will have to be suitably changed.
Given: Client’s portfolio for the investment:•
Growth stock fund
•
Income fund
•
Money market fund
Overall risk-index = weighted average of risk ratings of 3 funds. Max risk index assigned for the client = .05 Total amount to be invested = $800,000 Type of fund GSF IF MMF
% amount invested of total amount 20 TO 40 20 TO 50 ATLEAST 30
Risk rating
Expected yield (%)
.10 .07 .01
18 12.5 7.5
SOLUTION:Let the decision variables be X1 = Amount invested in growth stock fund. X2 = Amount invested in investment fund. X3 = Amount invested in money market fund. The objective function (FOR THE MAXIMIZATION OF YIELD) will be Max Z = .18X1 + .125X2 + .075X3. Subjected to the constraints:1. 160000 <= X1 <=320000 2. 160000 <= X2 <= 400000
3. X3 =>240000
4. (.1X1 + .07X2 + .01X3)/ (X1 + X2 + X3) <=.05 5. X1 + X2 + X3 =800000 1. On solving the above equations using management scientist, for the maximum yield, we have X1 = 248888, X2 = 160000, X3 = 391111 Z = 94133.33
2. Our new objective function is – Max Z = .18X1 + .125X2 + .075X3. And constraints are1. 160000 <= X1 <=320000 2. 160000 <= X2 <= 400000 3. X3 =>240000 4. (.1X1 + .07X2 + .01X3)/ (X1 + X2 + X3) <=.055 5. X1 + X2 + X3 =800000 On solving we getX1 = 293333, X2 = 160000, X3 = 346666 Z = 98800
3. Constraints are1. 160000 <= X1 <=320000 2. 160000 <= X2 <= 400000 3. X3 =>240000 4. (.1X1 + .07X2 + .01X3)/ (X1 + X2 + X3) <=.05 5. X1 + X2 + X3 =800000
A. New objective function isMax Z =.16X1+.125X2+.075X3
On solving we getX1=248888, X2=160000, X3=391111 Z= 89155
B. New objective function isMax Z=.14 X1 +.125 X2 +.075 X3 On solving we getX1=160000, X2=293333, X3=346666 Z=85066
4. Objective function isMax Z = .18X1 + .125X2 + .075X3. Subjected to the constraints:1. 160000 <= X1 <=320000 2. 160000 <= X2 <= 400000 3. X3 =>240000 4. (.1X1 + .07X2 + .01X3)/ (X1 + X2 + X3) <=.05 5. X1 + X2 + X3 =800000 6. X1<=X2
On solving this we getX1=213333, X2=213333, X3=373333 Z=93066
5. According to our recommendation, it is possible to use this model between the ranges:1. 15% < GROWTH STOCK FUND YIELD < NO LIMIT 2. NO LIMIT < INCOME FUND YIELD < 14.5% 3. 1.5% < MONEY MARKET FUND YIELD < 18%.
If the expected yield crosses these ranges, the model will have to be suitably changed.
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